The intercept of a line is the point at which is crosses either the x or y axis. If we do not specify which one, the y-axis is assumed. It is usually designated by the letter b. Unless that line is exactly vertical, it will always cross the y-axis somewhere, even if it is way off the top or bottom of the chart.

Formula for the intercept of a line

• Given the slope of the line and any point on the line

  The intercept (b) is given by

  where: m  is the slope of the line, found using methods described in Slope of a Line (Coordinate Geometry). x and y are the coordinates of any point on the line.

• Given two points on the line

  First calculate the slope using the methods described in Slope of a Line (Coordinate Geometry), and then use the method above to find the intercept.

Example

1. In the figure above press "reset".
2. Using methods described in Slope of a Line (Coordinate Geometry) find the slope of the line. In the figure above, you can click on "show slope" to see the slope calculation graphically. In this case, it is
   
3. Choose any point of the line, let's say B. The x and y coordinates of B are 40 and 25, so we put those into the formula as x and y, together with 0.5 for m:
   

Things to try

1. In the above diagram, Drag the points A and B around and notice how the intercept changes. Try it with A and B in different quadrants.
2. Click "hide details". Drag A and B to some new locations and calculate the intercept of the line yourself. Then click "show details" and see how close you got.

Equation of a line

For more on this see:

• Slope of a line
• Equation of a line

Other Coordinate Geometry entries

• Introduction to coordinate geometry
• The coordinate plane
• Coordinates of a point
• Distance between two points

• Introduction to Lines in Coordinate Geometry
• Lines (in Coordinate Geometry)
• Rays (in Coordinate Geometry)
• Line Segments (in Coordinate Geometry)
• Midpoint of a line segment (Midpoint Theorem)

• Distance from a point to a line - introduction
• - When line is horizontal or vertical
• - Using two line equations
• - Using trigonometry
• - Using a formula

• Slope (m) of a line
• Intercept (b) of a line
• Equation of a line in slope-intercept form y=mx+b
• Equation of a line in point-slope form y=m(x-Px)+Py

• Vertical lines
• Horizontal lines
• Parallel lines
• Perpendicular lines
• Intersecting lines

• Cirumscribed rectangle (bounding box)
• Area of a triangle (formula method)
• Area of a triangle (box method)
• Area of a polygon
• Area of a polygon (calculator)
• Rectangle
• Definition and properties, diagonals
• Area and perimeter
• Square
• Definition and properties, diagonals
• Area and perimeter
• Trapezoid
• Definition and properties, altitude, median
• Area and perimeter
• Parallelogram
• Definition and properties, altitude, diagonals

• Print blank graph paper